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    <title>arsimul</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : 16/12/2004</div>
    <p>
      <b>arsimul</b> -  armax simulation</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[z]=arsimul(a,b,d,sig,u,[up,yp,ep])  </tt>
      </dd>
      <dd>
        <tt>[z]=arsimul(ar,u,[up,yp,ep])  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>ar</b>
        </tt>: an armax process. See armac.</li>
      <li>
        <tt>
          <b>a</b>
        </tt>: is the matrix  <tt>
          <b>[Id,a1,...,a_r]</b>
        </tt>     of dimension (n,(r+1)*n)</li>
      <li>
        <tt>
          <b>b</b>
        </tt>: is the matrix <tt>
          <b>[b0,......,b_s]</b>
        </tt>      of dimension (n,(s+1)*m)</li>
      <li>
        <tt>
          <b>d</b>
        </tt>: is the matrix <tt>
          <b>[Id,d_1,......,d_t]</b>
        </tt>  of dimension (n,(t+1)*n)</li>
      <li>
        <tt>
          <b>u</b>
        </tt>: is a matrix  (m,N), which gives the entry u(:,j)=u_j</li>
      <li>
        <tt>
          <b>sig</b>
        </tt>: is a  (n,n) matrix  e_{k} is an n-dimensional Gaussian process with variance I</li>
      <li>
        <tt>
          <b>up, yp</b>
        </tt>: optional parameter which describe the past.  <tt>
          <b>up=[ u_0,u_{-1},...,u_{s-1}]</b>
        </tt>; 
          <tt>
          <b>yp=[ y_0,y_{-1},...,y_{r-1}];</b>
        </tt>
        <tt>
          <b>ep=[ e_0,e_{-1},...,e_{r-1}]</b>
        </tt>; 
          if they are omitted, the past value are supposed to be zero</li>
      <li>
        <tt>
          <b>z</b>
        </tt>: <tt>
          <b>z=[y(1),....,y(N)]</b>
        </tt>
      </li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    simulation of an n-dimensional armax process 
    <tt>
        <b>A(z^-1) z(k)= B(z^-1)u(k) + D(z^-1)*sig*e(k)</b>
      </tt>
    </p>
    <pre>
       A(z)= Id+a1*z+...+a_r*z^r;  ( r=0  =&gt; A(z)=Id)
       B(z)= b0+b1*z+...+b_s z^s;  ( s=-1 =&gt; B(z)=[])
       D(z)= Id+d1*z+...+d_t z^t;  ( t=0  =&gt; D(z)=Id)
    </pre>
    <p>
    z et e are in  <tt>
        <b>R^n</b>
      </tt> et u in <tt>
        <b>R^m</b>
      </tt>
    </p>
    <h3>
      <font color="blue">Method</font>
    </h3>
    <dl>
      <p>
    a state-space representation is constructed and ode with the option  "discr" is used to compute z</p>
    </dl>
    <h3>
      <font color="blue">Author</font>
    </h3>
    <p>J-Ph.C.</p>
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